grandes-ecoles 2015 QV.A.3

grandes-ecoles · France · centrale-maths1__mp Groups Group Actions and Surjectivity/Injectivity of Maps
We define $\hat{f}^\star$ on $G$ by composing $\hat{f}$ with $\Psi$: we set, for all $g \in G$, $\hat{f}^\star(g) = \hat{f}(\Psi(g))$.
Demonstrate that $\hat{f}^\star$ is $H$-invariant, that is, for all $g \in G$ and $h \in H$, $\hat{f}^\star(gh) = \hat{f}^\star(g)$. 
We define $\hat{f}^\star$ on $G$ by composing $\hat{f}$ with $\Psi$: we set, for all $g \in G$, $\hat{f}^\star(g) = \hat{f}(\Psi(g))$.

Demonstrate that $\hat{f}^\star$ is $H$-invariant, that is, for all $g \in G$ and $h \in H$, $\hat{f}^\star(gh) = \hat{f}^\star(g)$.
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.A.5 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QI.C.1 QI.C.2 QI.C.3 QI.C.4 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QIII.A QIII.B QIII.C.1 QIII.C.2 QIII.C.3 QIV.A.1 QIV.A.2 QIV.B.1 QIV.B.2 QIV.B.3 QIV.C.1 QIV.C.2 QIV.C.3 QIV.D.1 QIV.D.2 QIV.D.3 QV.A.1 QV.A.2 QV.A.3 QV.B.1 QV.B.2